$f(x)=-(x+3)(x+10)$ 1) What are the zeros of the function? Write the smaller $x$ first, and the larger $x$ second. $\text{smaller }x=$
Explanation: $\begin{aligned} -(x+3)(x+10)&=0 \\\\ x+3=0&\text{ or }x+10=0 \\\\ x={-3}&\text{ or }x={-10} \end{aligned}$ There are many ways to find the vertex. We will do it by using the fact that the $x$ -coordinate of the vertex is exactly between the two zeros. $\begin{aligned} \text{vertex's }x\text{-coordinate}&=\dfrac{({-3})+({-10})}{2} \\\\ &={-\dfrac{13}{2}} \end{aligned}$ Now we can find the vertex's $y$ -coordinate by evaluating $f\left({-\dfrac{13}{2}}\right)$ : $\begin{aligned} f\left({-\dfrac{13}{2}}\right)&=-\left({-\dfrac{13}{2}}+3\right)\left({-\dfrac{13}{2}}+10\right) \\\\ &=-\left(-\dfrac72\right)\left(\dfrac72\right) \\\\ &=\dfrac{49}{4} \end{aligned}$ In conclusion, $\begin{aligned} \text{smaller }x&=-10 \\\\ \text{larger }x&=-3 \end{aligned}$ The vertex of the parabola is at $\left(-\dfrac{13}{2},\dfrac{49}{4}\right)$